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How do you find the phase and inverse Fourier transform of this frequency spectrum?

  • 3
    $\begingroup$ Is this a homework assignment? $\endgroup$ – hotpaw2 Jun 23 '14 at 19:15
  • $\begingroup$ no it isn't.... $\endgroup$ – martinap Jun 23 '14 at 19:18
  • $\begingroup$ The spectrum is usually complex. Sometimes the definition implies "magnitude", which is real, but in that case it would be positive. Perhaps you could clear this up a little from the context of the book? In this meant to be a Fourier representation of a signal which happens to be purely real? $\endgroup$ – Phonon Jun 23 '14 at 22:45
  1. The magnitude is given by $ {\left| X \left( f \right) \right|} $ hence it is 6.
  2. Assuming all data is given in the graph, the function isn't complex it is only negative -> Phase is -180 degrees.
  3. You should use its symmetry. Without over thinking it, It could be generated by a window on the center convolved with 2 deltas (Shifted) -> Sinc in time multiplied by 2 exponentials.
  • 1
    $\begingroup$ The magnitude is $|X(f)|$, not $|X(f)|^2$ (which is the squared magnitude). So its value is 6, not 36. $\endgroup$ – Matt L. Jun 24 '14 at 7:43
  • $\begingroup$ By the book you're correct. Yet usually this term is abused, and I assumed this to be the case :-) (Since otherwise it would be seem trivial). Anyhow, fixed it. $\endgroup$ – Royi Jun 24 '14 at 7:48

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